[PD] ipoke~ ?

[Charles Henry]

On Wed, Jun 13, 2012 at 6:14 PM, katja <katjavetter at gmail.com> wrote:

> There should be an (optional) amplitude compensation for up- and
> downsampling, as an amplitude effect would be inconvenient in the case
> of a variable-speed sound-on-sound looper.
>
> Katja

I think that a consideration here to justify a scaling effect is to
deliver the same rate of power.

I like looking at this problem with sinc functions, because the
spectrum becomes easy to see, and the energy is easy to calculate.

The function with sampling rate f_s and unit spectrum from -f_s/2 to
f_s/2 is f_s*sinc(t*f_s).  This function when it's convolved with
itself, equals itself.

and if you have f1 < f2,  f1*sinc(t*f1) convolved by f2*sinc(t*f2) =
f1*sinc(t*f1)   which is important for comparing interpolators at
different frequencies.

The L2 norm of f_s*sinc(t*f_s) = f_s.
Here's the term that grows larger when we increase f_s.

In a given block, you're always writing N samples.  Your goal is to
write N orthogonal functions that fills all the values in some
interval and keep normalized the power during that interval.